There Are Only 14 Possible Calendar Configurations

At the beginning of every year, I get a tropical island wall calendar. During the winter, it makes the days seem warmer; during the summer, it inspires me to enjoy the long sunny days.

Until a few days ago, my January 2010 calendar was really small. I hadn’t bought a new calendar yet, so I was squinting at the tiny January 2010 layout in the corner of my December 2009 calendar.

If only I kept my 1999 calendar, I could have used that this year.

You see, there are only 14 possible calendar configurations. This year, January first was a Friday and next year, it’s a Saturday. In 2012 it’s a Sunday, but in 2013 it’s a Tuesday.

Why do we skip Monday? Because 2012 is a leap year, it pushes January first back a day in the following year. Leap years are also why the 14 calendar configurations do not fall in 14 consecutive years.

There are only two variables that differentiate one calendar from another:

the day of the week the year begins

whether or not it is a leap year

Lets say you want to collect all 14 calendars. You need one calendar that begins on each day of the week for both regular years and leap-years (7 x 2 = 14). If you time it right, you can get 9 of the calendars you need in 9 consecutive years. But, you’ll need to wait another 17 years to collect the remaining 5 leap year calendars that complete your collection.

Obviously, using old calendars isn’t practical. You probably have writing on them, or crossed off days leading up to a special date or counting the number of days you’ve stayed faithful to a resolution. Also, the moon phases will be horribly inaccurate. Moon phases repeat approximately every 29 days, 12 hours, 44 minutes — meaning they repeat about every nine years. Good luck trying to collect all of those calendars.

If you found this topic interesting, you might also enjoy my writing on leap seconds.

1972 repeats after 28 years because there are 14 different calendars but they do not rotate evenly because leap years have an extra day, and the first day of the year after a leap year will be two days on from the first day of the leap year. That way, as 1972 starts on a Saturday (the 7th day of the week) and is a leap year is well, it is the 14th possible calendar format. However, it takes more than 14 years between calendars because the pattern is disrupted by adding two days after every leap year. Because of this, a Saturday starting a leap year will not occur till 28 years time. It is the rarest of the calendar formats, occurring only 4 times a century.